# Definition of Fourier Series

French mathematician J.B.J. Fourier first studied the periodic function in 1822 and published his theorem which states that,

“Any arbitrary periodic function can be represented by an infinite series of sinusoids of harmonically related frequencies.” This infinite series is known as Fourier series.

Thus, if

*f*(*t*) is a periodic function, then the Fourier series is,*f*(

*t*) =

=

where,

*ω*is the fundamental frequency =*nω*is the

*n*

^{th}harmonic of fundamental frequency

*a*

_{0},

*a*

*,*

_{n}*b*

_{n}_{ }are the Fourier Co-efficients